Barack Obama with his wife, Michelle, at the White House in December 2011. Photograph: Jewel Samad/AFP/Getty Images

Three years ago to the day, Barack Hussein Obama stood before a crowd shivering in the frigid January air and took the oath of office that made him the 44th president of the United States. By some estimates, there were two million people thronging the National Mall in Washington that day, a human carpet stretching to the steps of the Capitol, to witness a moment many – perhaps most – never believed they would see: the inauguration of America's first black president. When Aretha Franklin, in a splendid hat, sang My Country, 'tis of Thee, the air filled with hope that this would be a moment of healing – of the immediate, bruising past of the Bush years, but also of the long history of racial division in America. Hopes, in other words, that were almost impossibly high.

And these vaulted ambitions did not only apply to the vexed matter of race. Time magazine's cover featured a photo-montaged image merging Obama and Franklin Roosevelt, hailing "the New New Deal". There was a breathless expectation that Obama was poised to solve an economic crisis with a programme of investment and government activism that would not only put Americans back to work but rebuild the country, preparing it for a cleaner, greener future. And of course Obama would put aside the reckless, swaggering foreign policy of his predecessor, would reach out to the Muslim world and would doubtless replace discord with harmony across the globe. It was not just those who were there on that bright January morning who got caught up in the excitement of all this promise. Less than nine months later, the Nobel committee gave Obama its peace prize.

Now all that seems a long time ago. Conservative Americans, especially those who live in the Foxosphere, never believed the hype anyway. But since then, many of the one-time true believers, Democrats and liberals, have lost their faith in Obama. They believe his presidency has been a terrible, historic letdown; that he has not delivered on his promises; that instead of bringing radical change, he has provided more of the same; that he has been a weak, querulous presence in the White House, unwilling to make enemies, unwilling even to define himself or make clear what he stands for.

The specific charge sheet against Obama could run for several pages and then several more. On the economy, the president is blamed for a lack of ambition, for passing a stimulus package of $787bn that, say the critics, should have been nearly twice the size. Obama erred, too, by allowing Democrats in Congress to write the stimulus bill, packing it with pet schemes and pork that would do little to get the economy moving. In an attempt to win Republican support – which never came – he also weighed down the bill with too many tax cuts. The result was action that was simply incomplete, leaving unemployment hovering around the 9% mark for most of Obama's presidency.

Former admirers say he was too weak on the banks, failing to declare war on those who had caused the 2008 crash. The clues were there in his senior appointments. While some liberals had fantasised about a dream ticket of Nobel laureate Paul Krugman and former labour secretary Robert Reich, Obama filled his two key economic posts with Larry Summers and Timothy Geithner, both schooled by Robert Rubin, former co-chair of Goldman Sachs. Obama did legislate on financial reform, but the bill did not go far enough, with no restoration of the Depression-era Glass-Steagall act, which had previously separated casino and retail banking. Nor was there any action to cap the pay of top executives, even in companies majority-owned by the US government. It's not that Obama fought and lost on these issues. In most cases, he did not even fight.

His signature achievement, the passage of healthcare reform, also dismayed as many liberals as it delighted, chiefly because Obama surrendered on the so-called public option which, while not exactly establishing an American NHS, would have at least offered a government-run insurance programme as an alternative to the private sector. That made Obama's bill no more radical than one proposed decades earlier by Richard Nixon, or the one passed by a certain Mitt Romney when he was governor of Massachusetts.

In his inaugural address Obama spoke often and poetically on climate change. He vowed to "harness the sun and the winds and the soil to fuel our cars and run our factories". But there has been no action and not even any serious advocacy. Aware that Republicans do not even believe there is an energy problem, he has shied away from offering a solution.

Those of us watching from afar have felt versions of this disappointment. Plenty of Guardian readers would have cheered when Obama used his first day in office to sign an order for the closure of the detention camp at Guantánamo Bay – and chose to make his first presidential phone call to the Palestinian president, Mahmoud Abbas. But, thwarted by a Republican refusal to allow any ex-Guantánamo detainees to set foot on US soil, Obama has been unable to make good on that day one order: Camp Delta remains open. As for Israel-Palestine, on which he had promised to work from his first day in office, the US role has been ineffective or even, by some lights, counter-productive.

"He has allowed himself to be an American president poked in the eye by Bibi," says one former European foreign minister who worked on the Middle East peace process, referring to the Israeli prime minister, Binyamin Netanyahu. Many diplomats and others agree that Obama's insistence on a freeze on Israeli settlement building, however well-intentioned, proved to be a tactical error, allowing any chance of progress to become entangled in one single aspect of what is a much larger problem – and that in the staring contest between Obama and Netanyahu, Obama blinked first. What explains these multiple failings? Are they the fault of Obama the man or of the system? On the domestic front, some are forgiving of the president, saying that he has faced impossible odds. Among the obstacles is an intransigent Republican party in Congress that does not hide its desire to deny Obama anything that looks like an achievement, even if such paralysis damages the national interest. "The single most important thing we want to achieve is for President Obama to be a one-term president," said the Republicans' senate leader, Mitch McConnell.

Add to that a senate rulebook that allows the Republican minority to filibuster and frustrate every Democratic initiative; a Democratic party as divided and factional as the Republicans are united and disciplined; a Fox News echo chamber that daily demonises the president as a Muslim Marxist foreigner eager to impose totalitarianism on the American republic; and corporate money ready to flood the airwaves and put pressure on the congressmen it funds to ensure its interests are protected. Viewed like this, Obama was only ever a mere mortal taking on an invincible machine – and so was always bound to fail.

Others are less charitable. They point first to Obama's tactical errors. He should never have let Congress write the healthcare bill, thereby delaying and diluting it, but should have taken the initiative himself. He should have focused on jobs before healthcare reform anyway. Above all, he tried to accommodate the Republicans for too long. He believed his own rhetoric, which promised an end to Washington partisanship – "he drank his own Kool-Aid," says one observer – when he should have rapidly realised that Republicans did not want to sit around the campfire with him singing Kumbaya. They wanted to destroy him. He should have drawn a clear dividing line between him and them, defining himself as the defender of the national interest and of the hard-pressed, and casting the Republicans as the enemy. He should have channelled the spirit of FDR, who did not hesitate to say of his political adversaries: "I welcome their hatred." Instead, he remained cool, calm and hyper-rational to a fault, often described as too chilly to connect emotionally with the nation he leads.

Which brings us closer to the core critique of Obama. That he avoids a fight, that he folds too early, that in his desire to unite and heal he too often surrenders his own position – to the point where no one is clear what his own position is. He blinked yet again when he faced down congressional Republicans who refused to raise America's debt ceiling last August, even though polls showed the US public backed him. "Every time the Republicans played chicken with him, he caved," laments Nation columnist Eric Alterman, who adds: "This is really painful for me. I loved the guy."

So the liberal disappointment with Obama is real. And yet it may not endure forever. Despite everything, the president has amassed quite a record. The healthcare reform he passed had eluded every president since Teddy Roosevelt; it had been a Democratic goal since Truman. But only Obama did it. The stimulus package has created an estimated 2.4m jobs and prevented the recession turning into a second Depression. While other advanced economies are caught in a downward spiral of deficit fetishism, the US is seeing unemployment come down. And recently, Obama successfully fought for and defended the payroll tax cut, one tax cut that benefits low-income Americans.

Abroad, Obama secured what George W Bush only blustered about: the removal of Osama bin Laden. Under Obama, al-Qaida's capacity and strength have diminished sharply. He made good on his promise to bring troops home from Iraq and is doing the same in Afghanistan (even if he is not so much ending the war there as simply pulling out). Yes, the US played a crucial back-up role in Libya, but there has been no repeat of Bush's warmongering.

It is not a bad record and there is every chance that it will represent merely the first half of a long game. If, as looks likely, Obama is re-elected in November, the FDR precedent might be invoked once again: it was in his second term that Roosevelt notched up some of his greatest achievements. This president, too, may have learned from his mistakes and got the true measure of his enemies. After three long, hard years, there are still grounds for hope.

• This article was amended on 20 January 2011. The original referred to Camp X-Ray, when Camp Delta was meant.